English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper is devoted to the study of the $M$-Wright function($M_{\alpha}(t)$) which is the inverse Laplace transform of thesingle-parameter Mittag-Leffler (ML) function ($E_{\alpha}(-s)$). Because$E_{\alpha}(-s)$ can be viewed as the fractional-order generalization of theexponential function for $0<\alpha<1$, to which it reduces for $\alpha=1$, i.e.$E_{1}(-s)=\exp(-s)$, its inverse Laplace transform, being $M_{\alpha}(t)$, canbe viewed as a generalized fractional-order Dirac delta function. At thelimiting case of $\alpha = 1$ the $M$-Wright function reduces to$M_{1}(t)=\delta(t-1)$. We investigate numerically the behavior of thisfractional-order delta function as well as it integral, the fractional-orderunit-step function. Subsequently, we validate our results with experimentaldata for the charging of a supercapacitive device.

Theory and Application of the Fractional-order Delta Function Associated with the Inverse Laplace Transform of the Mittag-Leffler Function